In a previous work, we defined the chiral screened vertex operators of W-algebra extended conformal theories by fusion of elementary ones. After reviewing how to obtain the braid group representation matrices, realizing the exchange algebra for those chiral vertex operators corresponding to the symmetric tensor representations of An, we generalize our results to chiral screened vertex operators associated with arbitrary An representations. The fused braiding matrices for antisymmetric tensor screened vertex operators are computed explicitly and shown to have a very simple form. Closure of the exchange algebra in the general case is proved using the relation with the Boltzmann weights of the An face models. Since, in the unitary case, the W-algebras are realized as cosets ĝk⊕ĝ1/ĝk+1, the present results can also be reinterpreted in terms of fusion of braiding matrices of the ĝ WZW models. As an example, the simplest W-algebra extended theory, the 3-state Potts model, is discussed in some detail.
Construction ofR-matrices for symmetric tensor representations related to ${U}_{q}(\hat{{{sl}}_{n}})$
